Pulse the peeled ginger and garlic in a food processor until finely chopped, then add the peeled onion and pulse until finely chopped as well; alternatively finely mince by hand.
Toss the diced chicken with 1 1/2 tsp garam masala and 1 tsp salt until evenly coated.
Heat 1 Tbsp olive oil in a large skillet over medium-high heat, add the chicken in a single layer, and cook, turning once, until cooked through about 6–7 minutes total; transfer the chicken to a plate.
Heat the remaining 1 Tbsp olive oil in the same skillet over medium-high heat, add the chopped onion mixture, and sauté until softened, about 3 minutes.
Add the tomato paste, the remaining 1 Tbsp garam masala, paprika, and cayenne; cook while stirring constantly for about 30 seconds to toast the spices.
Stir in the crushed tomatoes, season with additional salt to taste, and cook, stirring occasionally, until the sauce is hot and slightly thickened, about 2 minutes (longer if tomatoes are watery).
Return the cooked chicken to the skillet and cook for 1 more minute to heat through.
Remove the pan from the heat, stir in the Greek yogurt and lemon juice until smooth, then taste and adjust seasoning.
Serve warm over basmati rice and sprinkle with cilantro leaves.
